A286132 Expansion of q^(-1/2) * eta(q^3) * eta(q^10) * eta(q^14) * eta(q^105) in powers of q.

0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 1, -1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, -1, 1, -1, -1, -1, -1, 0, 0, 0, 2, -2, -1, -1, 1, 1, -1, -2, 0, -1, -1, 0, 1, 0, 1, 0, 2, -1, 0, 0, -1, 2, 0, 0, 0, 2, -1, 0, 0, 1, 0, 2, 1, 1, 0, 0, 2, 1, 0, -1, -1, 0

Offset

0,40

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Michael Somos, A Remarkable eta-product Identity

Formula

G.f.: x^5 * Prod_{k>0} (1 - x^(3 * k)) * (1 - x^(10 * k)) * (1 - x^(14 * k)) * (1 - x^(105 * k)).

Maple

seq(coeff(series(x^5*mul((1-x^(3*k))*(1-x^(10*k))*(1-x^(14*k))*(1-x^(105*k)), k=1..n), x, n+1), x, n), n=0..150); # Muniru A Asiru, Jul 29 2018

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; CoefficientList[Series[q^(-1/2)* eta[q^3]*eta[q^10]*eta[q^14]*eta[q^105], {q, 0, 50}], q] (* G. C. Greubel, Jul 29 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^3)*eta(q^10)*eta(q^14)*eta(q^105); concat(vector(5), Vec(A)) \\ G. C. Greubel, Jul 29 2018

Crossrefs

Cf. A286135.

Sequence in context: A331180 A126389 A278112 * A105551 A305195 A073772

Adjacent sequences: A286129 A286130 A286131 * A286133 A286134 A286135

Keyword

sign

Author

Seiichi Manyama, May 03 2017

Status

approved